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If a chord AB subtends and angle of 60^(...

If a chord `AB` subtends and angle of `60^(@)` at the centre of a circle, then the angle between the tangents to the circle drawn from `A` and `B` is

A

`30^(@)`

B

`60^(@)`

C

`90^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `P` be the point of intersection of tangents at `A` and `B`.
Then, `OAPB` is a cyclic quadrilateral.
`:. /_AOB+/_APB=180^(@)implies/_APB=180^(@)-60^(@)=120^(@)`.
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